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Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates

WORC, Tilburg University, The Netherlands

Rolf Langeheine

Institute for Science Education, University o f Kiel

Ulf Bockenholt

Department of Psychology, University o f Illinois, Urbana-Champaign

Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both time- constant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.

Key Words: categorical data • EM algorithm • latent class analysis • latent Markov models • log-linear models • logit models • measurement error • modified Lisrel approach • modified path analysis approach • panel analysis • time-varying covariates

Journal of Educational and Behavioral Statistics, Vol. 24, No. 2, 179-207 (1999)
DOI: 10.3102/10769986024002179


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